The Evolution and Outflows of
Hyper-Accreting Disks
Brian Metzger, UC Berkeley
with Tony Piro, Eliot Quataert & Todd Thompson
Metzger, Thompson & Quataert (2007), ApJ, 659, 561
Metzger, Quataert & Thompson (2008), MNRAS, 385, 1455
Metzger, Thompson & Quataert (2008), ApJ, 676, 1130
Metzger, Piro & Quataert (2008a), MNRAS in press
Metzger, Piro & Quataert (2008b), In preparation
Outline
 Introduction
 Compact Object Mergers and White Dwarf AIC
 Short GRBs: Recent Advances and New Puzzles
 Hyper-Accreting Disk Models
 One-Zone “Ring” Model
 1D Height-Integrated Model
 Disk Outflows and Nucleosynthesis
 Neutrino-Driven Winds (Early Times)
 Viscously-Driven Winds (Late Times)
 Conclusions
Compact Object Mergers (NS-NS or BH-NS)
Lattimer & Schramm 1974, 1976; Paczynski 1986; Eichler et al. 1989
t = 0.7 ms
“Chirp”
Shibata & Taniguchi 2006
t = 3 ms
• Inspiral + NS Tidal Disruption
– Primary Target for Advanced LIGO / VIRGO
•
•
•
•
Disk Forms w/ Mass ~ 10-3 - 0.3 M and Radius ~10-100 km
Hot ( kT > MeV) and Dense ( ~ 108-1012 g cm-3) Midplane
Cooling via Neutrinos: ( >>1,  ~ 0.01-100 )
Ý ~ 102 10M s-1  GRB Progenitor?
Accretion Rate M
Accretion-Induced
Collapse
Nomoto & Kondo 1991; Canal 1997
• Electron Capture (24Mg  20Ne  20O)
Faster than Nuclear Burning  O-Ne-Mg
White Dwarf Core Destabilized
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Dessart+06
776 ms post bounce
Md ~ 0.1 M Disk
Forms Around NS
Gamma-Ray Bursts: Long & Short Duration
BATSE GRBs
Long
• High Redshift: <z> ~ 2
• Large Energies (Eiso~1052-54 ergs)
• Star Forming Hosts
• Type Ibc Broad-Line Supernovae
Nakar 07
Short
2
1 H 
t visc 
 
K R 
1/ 2
M BH  0.1 R 3 / 2 H /R 2
 0.4 s 
 

  





 100 km
0.2 
3M 
Short GRB Host Galaxies
GRB050709
GRB050509b
Bloom+ 06
z = 0.16
SFR = 0.2 M yr-1
z = 0.225
SFR < 0.1 M yr-1
KECK Bloom+06
HUBBLE Fox+05
GRB050724
Berger +05
z = 0.258
SFR < 0.03 M yr-1
Berger+05
Short GRB Host Galaxies
GRB050709
GRB050509b
Bloom +06
z = 0.16
SFR = 0.2 M yr-1
No SN!
(But Some Radioactive
Ejecta Expected…)
z = 0.225
SFR < 0.1 M yr-1
KECK Bloom+06
HUBBLE Fox+05
• Lower z
• Eiso~ 1049-51GRB050724
ergs
Berger +05•
Older Progenitor
GRB050724
Population
z = 0.258
SFR < 0.03 M yr-1
Berger+05
Short GRBs with
Extended Emission
GRB050709
Who Ordered
That?!
- Regular ~ 30-100 s Duration
- Energy Often Exceeds GRB’s
- ~25% of Swift Short Bursts
BATSE Examples
Late-Time Flaring
(Norris & Bonnell 2006)
GRB050724
XRT, Campana+06
A “Ring” Model of Hyper-Accreting Disks
Metzger, Piro & Quataert 2008a
MÝ
BH
Vr < 0
Vr > 0
rd
Ý
• Mass at large radii ~ rd controls disk evolution and sets M

• Model enforces mass & angular momentum conservation
• Thermal Balance:
dS
T
 qÝvisc  qÝ
dt
qÝvisc 

9 2
 ,
4
Md
tvisc (rd )
 =  cs H
• Calculates {, T, H} @ rd(t) GIVEN rd,0, Md,0, MBH, and 

Simple model
 allows wide exploration of parameter space:
Initial disk mass/radius, viscosity , outflows, etc.
Three Phases of
Hyper-Accreting
Disks
2
3
1
Ý Thick Disk: H ~ R
1) High M
-
Optically Thick Matter Accretes Before Cooling
2) Neutrino-Cooled Thin Disk: H ~ 0.2 R

-
Ý c2
Optically Thin, Neutrino Luminosity L ~ 0.1 M
Ion Pressure Dominated / Mildly Degenerate e  p    n
e
Neutron-Rich Composition (n/p ~ 10)

Ý Thick Disk: H ~ R
3) Low M
-

e  n  e  p
Neutrino Cooling << Viscous Heating 

Radiation Pressure-Dominated / Non-Degenerate
Example Ring Model Solution
.
0.1 Mdc2 (1051 ergs)
T (MeV)
rd (km)

M (M s-1)
MBH = 3 M Md,0 = 0.1 M rd,0 = 30 km  = 0.1 tvisc,0 ~ 3 ms
Mdt-1/3
tthick
Late-Time Thick Disk Outflows
Advective disks are only marginally bound. When the disk cannot cool, a
powerful viscously-driven outflow blows it apart (Blandford & Begelman 1999).
Only a small fraction
of ingoing matter
actually accretes
onto black hole
BH
Hawley & Balbus 2002
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Nuclear energy from
-particle formation
also sufficient to
unbind disk
Effect of the Thick Disk Wind
Late-Time Short
GRB Activity
tthick?
• XRBs Make Radio Jets Upon Thermal (Thin Disk)
 Power-Law (Thick Disk) Transition
(e.g. Fender +99; Corbel + 00; Fender, Belloni, & Gallo 04; Gallo +04)
• Extended Emission = Thick Disk Transition?
• Problem: Requires Very Low Viscosity  ~ 10-3
23/17
tTHICK

  
~ 0.1 s  
0.1
 M d ,0 9 /17 rd ,0 9 / 34 M BH 1/ 2
 

 

0.1M  100 km 3M 
Other Sources of Extended Emission
Lee & Ramirez-Ruiz 07
Tidal Tail Fallback
Rosswog 06, Lee & Ramirez-Ruiz 07
Magnetar Spin-Down
Following AIC
P0= 1 ms
1016 G
GRB060614 Overlaid
Metzger, Quataert & Thompson 08

NS

EÝ

Ýc 2
M
High 
3 1015 G
Low 
1015 G
Disk Outflows & Heavy Element Synthesis
• GRB Jets Require Low Density, but High Density Outflows
Probably More Common  Heavy Element Formation
{n, p}   ' s  C  Fe - group  r - process?
12
• EBIND ~ 8 MeV nucleon-1  vOUT ~ 0.1-0.2 c
• Which Heavy Isotopes are Produced Depends on:
Electron Fraction Ye = np/(nn+np)
Ye
Product Nuclei
0.48 - 0.6 Mostly Ni56 - Ideal 9 Day Decay Time
0.4 - 0.48 Rare Neutron-Rich Isotopes (58Fe, 54Cr, 50Ti, 60Zn)
0.3 - 0.4
Very Rare Neutron-Rich Isotopes (78,80,82Se, 79Br)
< 0.3
r-Process Elements (e.g. Ag, Pt, Eu)
(Ye = 0.88)
(Ye ~ 0.5)
Rare Neutron-Rich
Isotopes (Ye ~ 0.3 - 0.4)
2nd/3rd Peak r-Process
(Ye < 0.3)
(Ye < 0.2)
Atomic Number (A)
Neutrino Heated Winds
Burrows, Hayes, & Fryxell 1995
Original Application: Core-Collapse Supernovae
(Duncan+ 84; Qian & Woosley 96; Thompson+ 01)
t = 0.5 s
Emergence of the
Proto-Neutron Star Wind
 e  n  e  p



p

e
n
e
• Neutrinos Heat & Unbind Matter from NS:
• Electron Fraction at  set by Neutrinos
n
p
– EBIND = 150 MeV, E ~ 15 MeV

 ~ 10 Neutrino Absorptions per Nucleon
NÝe  e n Le Ee
n


Ý
p
N e   e p L e E e
n
p
1


Le Ee

Ye  Ye  1

L
E
 e  e 

n
Neutrino-Driven Accretion Disk Winds
Levinson 06; Metzger, Thompson & Quataert 08
GMmn


IF
 E  THEN Ye  Ye
2R
GMmn
disk

IF
 E  THEN Ye  Ye
2R

Ýc2
L ~ 0.1 M

Ý
M Wind (R), Ye
Yedisk ~ 0.1
BH

Neutrino Luminosities L
e
/L e and Mean Energies E e /Ee
Ýdisk
Calculated Using a Steady - State Disk Model Given M
56Ni
Production in Neutrino-Driven Winds
1
rd
56Ni
10-1
GMmp/2R < E
Optically Thin @ RISCO
GMmp/2R > E
Accretion Rate (M s-1)
Optically Thick @ RISCO
Neutron-Rich
Isotopes
10-2
1
10
Wind Launching Radius (RISCO)
Metzger, Piro & Quatert 2008
Neutron-Rich Isotopes
Mini-Supernovae Following Short GRBs
Li & Paczynski 1998; Kulkarni 2005; Metzger, Piro & Quataert 2008a
Total 56Ni Mass Integrated
Over Disk Evolution:
(MNi ~ 10-3 M and Mtot ~ 10-2 M)
GRB050509b
(Hjorth +05)
V
J
Optical / IR Follow-Up  Initial Disk Properties
Metzger, Piro & Quataert 2008a
Metzger, Piro & Quataert 2008a
BH spin a = 0.9
Mini-SN Light Curve
Summary So Far
Neutrino-Cooled Thin Disk Phase
-
Neutron-Rich Midplane (Ye ~ 0.1)
-
Neutrino-Driven Wind  Up To ~ 10-3 M in 56Ni
 Mini-SN
(+ even more neutron-rich matter from larger radii)
Late-Time Thick Disk Phase
-
Viscously-Driven Wind Disrupts Disk
-
Disk Composition?? Wind Composition??
Late-Time Disk Composition:
Metzger, Piro & Quataert 2008b
Disk Thickening  Weak Freeze-Out
The Thick Disk Transition
Degeneracy
Pair Captures:
e  p   e  n
e   n  e  p
H/R
Yeeq
Ye


Both Cool Disk AND
Change Ye
Weak Freeze Out  Non-Degenerate Transition
 Moderately Neutron-Rich Freeze-Out (Ye ~ 0.25 - 0.45)
1D Height-Integrated Disk Calculations
Equations
Md,0 = 0.1 M, rd,0 = 30 km,  = 0.3
Local Disk Mass r2 (M)
Angular Momentum /
Continuity
Entrop
y
Heating
Cooling
Nuclear Composition
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Weak Freeze-Out
(A “Little Bang”)
Weak Interactions
Drive Ye  Yeeq
Until Freeze-Out
Electron Fraction
Ye
Yeeq
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Thickening / Freeze-Out Begins at the Outer Disk and Moves Inwards
Neutron-Rich Freeze-Out Is Robust
M per bin
M0 = 0.1 M,  = 0.3
Mtot = 0.02 M
M0 = 0.1 M,  = 0.03
Mtot = 0.02 M
M per bin
M0 = 0.01 M,  = 0.3
Mtot= 2 10-3 M
 ~10 - 30% of Initial
Disk Ejected Into ISM
with Ye ~ 0.2-0.4
Production of Rare Neutron-Rich Isotopes
Hartmann +85
40 Million Times
Solar Abundance!!!
0.35 < Ye < 0.4
 78,80,82Se, 79Br
Ye = 0.5
=1-2Ye
Ye = 0.4
Ye = 0.35
Merger Rates and the Short GRB Beaming Fraction
Metzger, Piro & Quataert 2008b
1
 M d ,0  1



5
1
NÝmax ~ 10   
 yr galaxy
0.2  0.1M 

1
From known merging NS
systems, Kim+06 estimate:
NÝNSNS = 3 105  2 104 yr -1

Milky Way Short GRB Rate ~ 10-6 yr-1 (Nakar 07)

   M d ,0 
NÝSGRB
fb 
 0.13  

Ý
0.2 0.1M 
N
 max
Jet Opening Angle  > 300
Short GRBs Less Collimated than Long GRBs (LGRB~2-100)

(Grupe +06; Soderberg +06)
Timeline of Compact Object
Mergers
1)
2)
3)
Inspiral, Tidal Disruption & Disk Formation (t ~ ms)
Optically-Thick, Geometrically-Thick Disk (t ~ ms)
Geometrically-Thin Neutrino-Cooled Disk (t ~0.1-1 s)
- Up to ~ 10-3 M in 56Ni from neutrino-driven winds (mini-SN)
4)
Radiatively Inefficient Thick Disk (t > 0.1-1 s)
- Degenerate  Non-Degenerate
- PGAS-Dominated  PRAD-Dominated
- Neutron-Rich Freeze-Out
Disk Blown Apart by Viscously-Driven Outflow
- Creation of Rare Neutron-Rich Elements (“Little Bang”)
From AIC Disk Winds
 Neutrino absorptions don’t affect Ye
strongly in compact merger disks
 BUT In AIC, e “flash” from shock
break-out can drive Ye > 0.5
e  n  e  p

Freeze-Out Ye in AIC Disk
With e Flash
Neutrino Luminosity (ergs s-1)
56Ni

Dessart+ 06
L e
“Flash”
Le
Time After Core Bounce (s)

 Winds synthesize ~10-2 M in 56Ni
 Optical Transient Surveys:
~ few yr-1 Pan-STARRs & PTF
No e Flash
~ 100’s yr-1 LSST
 Neutron-rich material also
synthesized?  unusual spectral
lines? (e.g, Zn, Ge, Cu?)
Conclusions
 Isolated Disk Evolution Cannot Explain Late-Time
X-Ray Emission (unless  ~ 10-3)
 Promising alternatives: Tidal tail fall-back and
magnetar spin-down
 Neutrino-driven winds create up to ~10-3M in 56Ni
 Mini-SN at t ~ 1 day
 Neutron-Rich Nucleosynthesis
 CO merger rate: < 10-5 yr-1 (Md,0/0.1 M)-1
 Short GRB jet opening angle:  > 30(Md,0/0.1 M)1/2
 ~10-2 M in 56Ni from White Dwarf AIC
 Target for upcoming optical transient surveys
Future Progress
Observations
Gravitational Waves
(LIGO; VIRGO)
Short GRB Optical / IR
Follow-Up
Spectroscopy of MetalPoor Halo Stars
Optical Transient
Surveys
Theory
MHD Disk Simulations:
Freeze-Out and LateTime Winds
Neutron-Rich
Nucleosynthesis
Compact Object
Merger Simulations
Spectra of Neutron-Rich
Explosions
Late-Time Optical Rebrightening: Mini-Supernova?
GRB060614; Mangano+07
Merger Rates and the GRB Beaming Fraction
• If a fraction  ~ 0.1 of initial disk mass is ejected with Ye < 0.4 per event:
NÝ   M d,0 X  t galaxy
X 
For tgalaxy = 10 Gyr and MISM = 109 M:
M ISM
From known merging NS
systems, Kim+06 estimate:
NÝNSNS = 3 105  2 104 yr -1
Milky Way Short GRB Rate ~ 10-6 yr-1 (Nakar 07)

Jet Opening Angle  > 100
Short GRBs Less Collimated than Long GRBs (LGRB~2-100)